Background Rate
Gem-5 User’s Manual 275
alarming is based on the instrument as a whole, that is, on the system of multiple
detectors.
Specifically, for a given K Alpha factor, the probability of false alarming will be
union of individual events of false alarming of the detectors in the system.
Given the independence of events the probability of FAR of the system can be
calculated as follow:
Equation 17 Calculation of FAR for a System With n Detectors
(17)
…where
is the number of detectors
Therefore, if Equation 15on page 273 is used to compute a confidence level for a
single detector, the value of K Alpha must be increased as the union of the events for
all detectors to maintain the desired confidence level.
It is worth noting, based on Equation 29 on page 289, that the required counting time
T
m
is related to the square of K Alpha.
Alarm Settings and Strategy starting on page 285 contains a more detailed
explanation of the system FAR.
K Beta - Positive Alarm Due to Contamination
Equation 28 on page 287 defines the Alarm Trip Point, ATP. The k factor for this
equation is defined as K Beta. To ensure that there is a least 95% confidence level of
alarming for actual contamination at exactly the release limit (i.e. not missing a true
alarm condition), the value of K Beta is set to 1.960 or greater (the default value is
2.00).
It is worth noting, based on Equation 29 on page 289 that the required counting time
T
m
is related to the square of K Beta.
Note that for increased levels of contamination in excess of the Alarm (Release)
Limit, the confidence level increases rapidly and approaches 1.
K Delta - Change in Background Rate
Equation 23 on page 278 describes the allowable statistical deviation in the
background before one assumes a significant change in the average background rate
has occurred. The confidence level is defined in Equation 22 and Equation 23 by the
factor K Delta. For the default K Delta value of 4.0 (for the Beta/Gamma Channels)
one would expect that only 1 in 16 thousand (1:16,000) background events would fall
outside the defined interval.
Background Rate
Background Rate Calculations
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